Monday, 23 September 2013

integration - How to show the following inequality in Measure Theory

How to show the following inequality in Measure Theory:





If $f$ is a non-negative measurable function defined on a measurable set $E$ then for any $\lambda >0$ we have $m\{x\in E:f(x)>\lambda \}\le\frac{1}{\lambda}\int _E f$ where $m$ denotes measure of a set




I can't figure out how to approach the above problem.Please give some hints.

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